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Calculated Risks: How to Know When Numbers Deceive You [Paperback]

Gerd Gigerenzer
3.5 out of 5 stars  See all reviews (2 customer reviews)
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Book Description

5 Jun 2002 0743254236 978-0743254236
At the beginning of the twentieth century, H. G. Wells predicted that statistical thinking would be as necessary for citizenship in a technological world as the ability to read and write. But in the twenty-first century, we are often overwhelmed by a baffling array of percentages and probabilities as we try to navigate in a world dominated by statistics. Cognitive scientist Gerd Gigerenzer says that because we haven't learned statistical thinking, we don't understand risk and uncertainty. In order to assess risk -- everything from the risk of an automobile accident to the certainty or uncertainty of some common medical screening tests -- we need a basic understanding of statistics. Astonishingly, doctors and lawyers don't understand risk any better than anyone else. Gigerenzer reports a study in which doctors were told the results of breast cancer screenings and then were asked to explain the risks of contracting breast cancer to a woman who received a positive result from a screening. The actual risk was small because the test gives many false positives. But nearly every physician in the study overstated the risk. Yet many people will have to make important health decisions based on such information and the interpretation of that information by their doctors. Gigerenzer explains that a major obstacle to our understanding of numbers is that we live with an illusion of certainty. Many of us believe that HIV tests, DNA fingerprinting, and the growing number of genetic tests are absolutely certain. But even DNA evidence can produce spurious matches. We cling to our illusion of certainty because the medical industry, insurance companies, investment advisers, and electioncampaigns have become purveyors of certainty, marketing it like a commodity. To avoid confusion, says Gigerenzer, we should rely on more understandable representations of risk, such as absolute risks. For example, it is said that a mammography screening reduces the risk of breast cancer by 25 percent. But in absolute risks, that means that out of every 1,000 women who do not participate in screening, 4 will die; while out of 1,000 women who do, 3 will die. A 25 percent risk reduction sounds much more significant than a benefit that 1 out of 1,000 women will reap. This eye-opening book explains how we can overcome our ignorance of numbers and better understand the risks we may be taking with our money, our health, and our lives.
--This text refers to an out of print or unavailable edition of this title.

Frequently Bought Together

Calculated Risks: How to Know When Numbers Deceive You + Risk Savvy: How To Make Good Decisions + Gut Feelings: Short Cuts to Better Decision Making
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Product details

  • Paperback: 324 pages
  • Publisher: Simon & Schuster (5 Jun 2002)
  • Language: English
  • ISBN-10: 0743254236
  • ISBN-13: 978-0743254236
  • Product Dimensions: 22.6 x 14.8 x 2.1 cm
  • Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 128,184 in Books (See Top 100 in Books)

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During a routine medical visit at a Virginia hospital in the mid-1990s, Susan, a 26-year-old single mother, was screened for HIV. Read the first page
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Most Helpful Customer Reviews
3 of 3 people found the following review helpful
2.0 out of 5 stars Duplicate of another work 3 Aug 2013
Don't get me wrong, the content of this work is worth 4 1/2 or 5 stars. It clearly lays out the common misconceptions that lead to many professionals misinterpreting conditional probabilities - if Gigerenzer's natural frequencies method was adopted by those required to interpret statistical results for the layman then I believe much less confusion would exist. However this book is word for word identical to another of Gigrenzer's books on the subject 'Reckoning with Risk' - I don't mean similar to I mean absolutely identical. I suspect they are the same book with different titles for different markets, however, misled by the Amazon recommendation 'frequently bought together' I now have a copy of both - it would have been nice to have seen this information displayed in the Book description of one of them (they even have different ISBNs). Mine will be up for sale shortly - don't buy it if you already have the other one!
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1 of 1 people found the following review helpful
5.0 out of 5 stars Eye opener 2 April 2012
By Grants
Format:Paperback|Verified Purchase
This book is an eye opener. It can be easily understood, enabling critical thinking and cross examination of what we are told by the medical profession. Very good 'other side of the coin' training for when we inevitably have to make life long committed decisions with our medical practitioners.
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Amazon.com: 4.5 out of 5 stars  26 reviews
39 of 39 people found the following review helpful
5.0 out of 5 stars How to interpret test results better than your Doc! 3 Jun 2004
By Gaetan Lion - Published on Amazon.com
Format:Hardcover|Verified Purchase
This is a very clearly written book. It demonstrates many numerical errors the press, the public, and experts make in interpreting the accuracy of medical screening test (mammography, HIV test, etc...) and figuring out the probability of an accused person being guilty.
At the foundation of the above confusions lies the interpretation of Baye's rule. Taking one example on page 45 regarding breast cancer. Breast cancer affects 0.8% of women over 40. Mammography correctly interprets 90% of the positive tests (when women do have breast cancer) and 93% of the negative ones (when they don't have breast cancer). If you ask a doctor how accurate this test is if you get a positive test, the majority will tell you the test is 90% accurate or more. That is wrong. The author recommends using natural frequencies (instead of conditional probabilities) to accurately interpret Baye's rule. Thus, 8 out of every 1,000 women have breast cancer. Of these 8 women, 7 will have a positive mammogram (true positives). Of, the remaining 992 women who don't have breast cancer, 70 will have a positive mammogram (false positives). So, the accuracy of the test is 7/(7+70) = 10%. Wow, that is pretty different than the 90% that most doctors believe!
What to do? In the case of mammography, if you take a second test that turns positive, the accuracy would jump to 57% (not that much better than flipping a coin). It is only when taking a third test that also turns positive that you can be reasonably certain (93% accuracy) that you have breast cancer. So, what doctors should say is that a positive test really does not mean anything. And, it is only after the third consecutive positive test that you can be over 90% certain that you have breast cancer. Yet, most doctors convey this level of accuracy after the very first test!
What applies to breast cancer screening also applies to prostate cancer, HIV test, and other medical tests. In each case, the medical profession acts like the first positive test provides you with certainty that you have the disease or not. As a rule of thumb, you should get at least a second test and preferably a third one to increase its accuracy.
The author comes up with many other counterintuitive concepts. They are all associated with the fact that events are far more uncertain than the certainty that is conveyed to the public. For instance, DNA testing does not prove much. Ten people can share the same DNA pattern.
Another counterintuitive concepts is associated with risk reduction. Let's say you have a cancer that has a prevalence of 0.5% in the population (5 in 1,000). The press will invariably make promising headline that a given treatment reduces mortality by 20%. But, what does this really mean? It means that mortality will be reduced by 1 death (from 5 down to 4). The author states that the relative risk has decreased by 20%; but, the absolute risk has decreased by only 1 in 1,000. He feels strongly that both risks should be conveyed to the public.
The author shows how health agencies and researchers express benefits of treatments by mentioning reduction in relative risk. This leads the public to grossly overstate the benefits of such treatment. The author further indicates how various health authorities use either relative risk or absolute risk to either maximize or minimize the public's interpretation of a health risk. But, they rarely convey both; which is the only honest way to convey the data.
If you are interested in this subject, I strongly recommend: "The Psychology of Judgment and Decision Making" by Scott Plous. This is a fascinating book analyzing how we are less Cartesian than we think. A slew of human bias flaws our own judgment. Many of these deal with other application of Baye's rule.
20 of 20 people found the following review helpful
5.0 out of 5 stars Be an Informed Consumer in the Age of Numbers 28 May 2003
By J. Williamsen - Published on Amazon.com
Format:Hardcover|Verified Purchase
Gerd Gigerenzer has written several books dealing with "bounded rationality"--how humans use their brains to understand the world around them, make decisions, and determine the risks associated with a given course of action. This book is easily his most accessible. It is clear and easy to read, with most(but not all)the examples drawn from the field of personal health.
Gigerenzer provides the simple mental tools that allow anyone to make sense of the statistics that bombard us daily in the media. It is exactly his point that one does not need to be a rocket scientist (or professional statistician) to understand the numbers used by professionals, from personal physicians to DNA experts, that affect our lives and livelihoods.
If I could recommend only one book to address "numerical illiteracy," this would be it. You will learn some essential skills in a clearly informative and entertaining way.
20 of 20 people found the following review helpful
5.0 out of 5 stars Required reading for everyone! 10 July 2002
By A Customer - Published on Amazon.com
In a valiant effort to educate professionals and lay people alike, the author of this book clearly explains how to interpret risks and risk data (statistics) in a useful and understandable way. For example, anyone who is wondering about whether or not to undergo screening for breast cancer, prostate cancer, HIV, etc. should do themselves a great big favor and read this book. The author also discusses legal issues such as how evidence may presented in court in order to support a given side of a case just by presenting statistical data, e.g., fingerprints, DNA evidence, etc., in certain ways. In addition, the author discusses a variety of other matters from advertising gimmicks to TV game show strategies. Using the techniques given in this book, readers will be much less likely to be fooled. Clearly written in plain english and in an engaging style, this book should be required reading for everyone - from professionals who provide statistical (risk) information (they would learn how to be more clearly understood) to those receiving the information (they would learn to see through any smoke screens or awkward presentations and thus make better decisions).
11 of 12 people found the following review helpful
5.0 out of 5 stars The truth about, fingerprints, DNA, AIDS, legal drugs, and so much more. 28 Dec 2005
By Dad Ditty - Published on Amazon.com
The book "Calculated Risk: How to Know When Numbers Deceive You", by Gerd Gigerenzer, will increase your risk aptitude. The 4 1/2 star (Amazon.com) book does not discuss statistical innumeracy from the IT perspective, but discusses innumeracy mainly in contemporary medicine, the justice system, and life in general.

Gerd describes four aspects of innumeracy as follows:

01) Illusion of certainty:

For example: Fingerprint and DNA testing.

02) Ignorance of relevant risks:

For example: "It is more likely that a young American male

knows baseball statistics than that his chances of dying on

a motorcycle trip is about 15 times higher than his chances

of dying on a car trip of the same distance."

03) Miscommunication of risks:

For example: One can communicate the chances that a test

will actually detect a disease in various ways ... The most

frequent way is in the form of a conditional probability: If

a person has cancer, the probability the he/she will test

positive on a screening is 90 percent. Many physicians

confuse that statement with this one: If a person test

positive on a screening, the probability that he/she has

cancer is 90 percent.

04) Drawing incorrect inferences from statistics:

For example: "Consider a newspaper article in which it is

reported that men with high cholesterol have a 50 percent

higher risk of heart attack. The figure of 50 percent

sounds frighting, put what does it mean? It means that out

of 100 fifty-year-old men without high cholesterol,

about 4 are expected to have a heart attack within ten years,

whereas among men with high cholesterol this number is 6. The

increase from 4 to 6 is the relative risk increase, that is,

50 percent. However. if one instead compares the number of

men in the two groups who are not expected to have heart

attacks in the next 10 years, the same increase in risk is

from 96 to 94, that is, about 2 percent (absolute risk). Now

the benefit of reducing one's cholesterol level no longer

looks so great."

Far from being a dry book on risk, uncertainty, and statistics, Gerd Gigerenzer is entertaining, provocative, irreverent and a bit of a maverick


" ... 1 out of every 90 Americans will lose his or her life in a motor vehicle accident by the age of 75. Most of them die in passenger car accidents."

" ... the terrorist attack on September 11. 2001, cost the lives of some 3,000 people. The subsequent decision of millions to drive rather than fly may have cost the lives of many more."

"... DNA ... match probability of 1 in 16 for a brother ... "

This book provides "tools for overcoming innumeracy that are easy to learn, apply, and remember."
51 of 67 people found the following review helpful
3.0 out of 5 stars Miscalculations or Misinterpretations? 28 Sep 2002
By Wayne C. Lusvardi - Published on Amazon.com
This is perhaps the best book at simply explaining the statistics of risk and uncertainty I have run across. I have even used what the author calls the illusion of certainty in analyzing the highest and best use of real estate. This book shows how medical experts and criminologists can be misled, not so much by innumeracy, as by what might better be called an illusion of expertise. Experts in any field may find this book useful in view of the U.S. Supreme Court's Daubert Rule that expert courtroom testimony must follow the scientific method.
A couple of caveats are in order however, and they are, shall we say, doozies. Gigerenzer states that there is ample evidence that smoking causes lung cancer. But he fails to consider why people from Asian and Pacific-Island cultures have some of the highest smoking rates in the world, but some of the lowest cancer rates. Any why do longitudinal studies show that people from these same cultures have much higher rates of cancer once they migrate to modern countries? Is it diet, smoking, a combination of the two, or something else that "causes" cancer? Likewise, Gigerenzer states that there is strong evidence that secondhand smoke is harmful to health. But he fails to mention the cardinal rule of toxicology: the dose, or concentration of a substance, makes the poison, not the substance itself. It is only in modern energy efficient air-tight buildings that smoke can be sufficiently concentrated so as to become an irritant, let alone a perceived health hazard. Thus, it may not be secondhand smoke, but the environment of tight buildings that is the source of the problem.
Thus, Gigerenzer fails to point out that all statistics and numbers must be actively interpreted and are relative in meaning to the interpreter. This involves a social filtering process not discussed in the book. Also, government may legitimate some health and crime statistics, when they may be bogus. As an aficionado of Gigerenzer's books, maybe he will write a sequel on the interpretation, misinterpretation, and social and political construction of statistics.
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